This article discusses how entropy/information methods are well-suited to analyzing and forecasting the four processes of innovation, transmission, movement, and adaptation, which are the common basis to ecology and evolution. Macroecologists study assemblages of differing species, whereas micro-evolutionary biologists study variants of heritable information within species, such as DNA and epigenetic modifications. These two different modes of variation are both driven by the same four basic processes, but approaches to these processes sometimes differ considerably. For example, macroecology often documents patterns without modeling underlying processes, with some notable exceptions. On the other hand, evolutionary biologists have a long history of deriving and testing mathematical genetic forecasts, previously focusing on entropies such as heterozygosity. Macroecology calls this Gini-Simpson, and has borrowed the genetic predictions, but sometimes this measure has shortcomings. Therefore it is important to note that predictive equations have now been derived for molecular diversity based on Shannon entropy and mutual information. As a result, we can now forecast all major types of entropy/information, creating a general predictive approach for the four basic processes in ecology and evolution. Additionally, the use of these methods will allow seamless integration with other studies such as the physical environment, and may even extend to assisting with evolutionary algorithms.These alternatives or 'alleles' can be characterized by the probabilities P(T) and P(A) in the biological population (usually at any position in the DNA, called a 'SNP' or single nucleotide polymorphism, only two of the possible four nucleotides are found). These molecular variants are exactly analogous to alternative species in ecological assemblages, and in most cases, measures or forecasts made in one of these areas have been, or could be, transferred directly to the other.This article will discuss how entropy/information methods are well suited to analyzing and forecasting the four common processes of innovation, transmission, movement, and adaptation in ecology and evolution. Despite the focus on a few variant types, this will apply broadly to variants of all types: DNA, epigenetics, behavior, species, the physical environment, etc., as well as their interactions [2,3].
Background: Measuring Biological Entropy, Information and DiversityMeasurement of ecological or evolutionary variants uses various entropy or information measures (Table 1a). The measures are all part of a 'q-profile' derived from a general power-sum of variant proportions (0 ≤ q ≤ ∞) [4,5]), composed of q D measures on a common scale of the 'effective' number of variants, which means the number of equally-frequent variants that would give the same entropy ( q H) as the typically unequal array of variants in the sampled system. The use of the q D profile has been recommended because each q value emphasizes different aspects of the diversity [6,7]; for example, higher q ...